Quantum Simulation with a Boson Sampling Circuit

TL;DR

This paper demonstrates how a boson sampling circuit embedded in two architectures can simulate bipartite XY spin models, including dissipative effects, and can be used to prepare boson sampling states in matter qubits.

Contribution

It introduces a method to simulate bipartite spin models using matter qubits coupled via a boson sampling circuit, including dissipation effects and state preparation.

Findings

Quibit evolution follows bipartite XY spin Hamiltonians.

Existence of many dark states with analytically estimable decay rates.

Potential for adiabatic preparation of boson sampling states.

Abstract

In this work we study a system that consists of $2M$ matter qubits that interact through a boson sampling circuit, i.e., an $M$-port interferometer, embedded in two different architectures. We prove that, under the conditions required to derive a master equation, the qubits evolve according to effective bipartite XY spin Hamiltonians, with or without local and collective dissipation terms. This opens the door to the simulation of any bipartite spin or hard-core boson models and exploring dissipative phase transitions as the competition between coherent and incoherent exchange of excitations. We also show that in the purely dissipative regime this model has a large number of exact and approximate dark states, whose structure and decay rates can be estimated analytically. We finally argue that this system may be used for the adiabatic preparation of boson sampling states encoded in the matter qubits.